Fundamentally, design is the wrong analogy. In design, there is a designer, and then there is something being designed. In society, the "designer" is already part of society, and he doesn't have the same degree of control an actual designer has.
Let's suppose you assemble everyone together to agree on and implement a design. The design process literally turns into a political process: a competitive effort to benefit fundamentally unreconcilable private interests and opinions rather than a collaborative effort to come up with an objectively good system. Stable, democratic governments aren't designers: they're a manifestation of the powers that be in the society already.
What form of government is a designer? The closest match seems to be some sort of brute-force colonialism--when foreigners try to redesign a society that they, themselves, are not a part of. The next-closest analogy to design is absolute dictatorship. Once you get into stable systems of government, even one-party states like China, or mature colonial states, but especially democracies, the political and economic system governing society is the result of a competitive game between different players, not the result of anyone implementing a design. Framing social problems in design terms is fundamentally wrong--well-functioning societies do not work that way and societies that are designed turn into bloodbaths until reverting to a form of society that's not designed.
I'm not unsympathetic to your viewpoint. I like to design things, too. Unfortunately, some things just can't be designed. There's a process fundamentally dissimilar to design--natural selection--that ultimately produced the human brain out of competing, uncoordinated forces following shallow goals. And when you put humans together in a social context, there are processes fundamentally dissimilar to design, made out of competing, uncoordinated forces, that ultimately produced liberal democracies. The biggest joke on the designer ever is that these undesigned processes eventually end up doing a better job than any designer would, as the blood-soaked social designers of the 20th century discovered.